Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 14, No. 2, pp. 569--581 (2004)

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On the principal bundles over a flag manifold

Hassan Azad and Indranil Biswas

Hassan Azad
Department of Mathematical Sciences
King Fahd University
Dhahran 31261
Saudi Arabia
Indranil Biswas
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
Bombay 400005

Abstract: Let $P$ be a parabolic subgroup of a semisimple simply connected linear algebraic group $G$ over $\mathbb C$ and $\rho$ an irreducible homomorphism from $P$ to a complex reductive group $H$. We show that the associated principal $H$--bundle over $G/P$, associated for $\rho$ to the principal $P$--bundle defined by the quotient map $G\, \longrightarrow\, G/P$, is stable. We describe the Harder--Narasimhan reduction of the $G$--bundle over $G/P$ obtained using the composition $P\, \longrightarrow\, L(P)\, \longrightarrow\, G$, where $L(P)$ is the Levi factor of $P$.

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Electronic version published on: 1 Sep 2004. This page was last modified: 1 Sep 2004.

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